Zeitgeist The Movie, really three movies, is a film that attempts to demonstrate that several widely-believed things are myths. The first film deals with Christianity. Broadly, it begins by claiming that Jesus is nothing more than a "Sun God" in new clothes, and presents lots of arguments to support this, and then ends with a brief sidebar about how Christianity, specifically the Catholic Church, was created through political motives at the Council of Nicea. While it's true that the Council of Nicea was likely put together for political motives, and it's also true that the Catholic Church has a several blotches on its permanent record, one can't claim, based on the evidence in the film, that Jesus is a Sun God and that Christianity is merely a re-packaging of old Egyptian beliefs.
The film presents many similarities between astrology, sun-worship, and Jesus. First, it identifies many deities who share similar characteristics with Jesus, namely a birthday on or near the winter solstice, various nicknames such as "Prince of Peace", death then resurrection, and other similarities. The film proceeds to discuss how many icons and themes associated with Jesus are reminiscent of astrology, such as Christian artwork showing a cross and halo behind Jesus's head resembles the zodiacal chart. There are, however, some flaws with these arguments.
First, artwork showing cross and halo behind Jesus's head, is said to resemble a pagan symbol of a cross inscribed in a circle.
This symbol is shorthand for the sun and 12 zodiacal signs. The problem with this argument is that a symbol can have different meanings in different contexts. For example, the word "cong" would be pronounced "kong" (or maybe "song") if it were an English word, but in Mandarin Pinyin it'd be pronounced "tsong". One can't claim that the "c" in that word has any special significance, or that it somehow connects English and Mandarin. What happened is the Pinyin co-opted the symbol but gave it a new meaning. This is co-opting is a common theme in early Christian history: the incorporation of old ideas re-interpreted in a new light was often used as a tool to make Christianity more palatable to the new converts. Furthermore Christ was crucified; it stands to reason that he might be depicted on a cross. Is the cross a pagan symbol? Certainly, but we need to be careful not to reason in a circle: Do Catholics believe that Christ was crucified on a cross because crosses are an old symbol, re-used for a new story? Or was he crucified on a cross because the Romans used crosses, since crosses were already (astrologically) significant? Christ either died on the cross because that's a good way to tell the story, thus incorporating a pagan symbol (as the film says), or else Christ died on the cross because the symbol was important to his killers. The film itself claims that the cross was already important to the legions of sun worshippers; the fact that there is a similarity is not proof of a connection.
Another problem this film has is that it blindly accepts that Jesus was born on the 25th of December. Even the Catholic Church admits that they don't know when he was born. The early Church didn't even celebrate his birth but rather his conception. In the 4th century his conception was believed to be March 25th because the Church believed that he DIED on the 25th, and all prophets must live a whole number of years. The Bible doesn't tell us when Christ was born, the Church doesn't know, nobody knows. The Church claims that Christ's birthday was chosen to be on the same day as a pre-existing "Sun God" holiday, the feast of the Unconquered Sun. Again, this was done not because Jesus was a Sun god, but because the parallels made the new religion easier to accept for the new converts. Linking Christ's birth to the astronomical events (Sirius lining up with Orion's belt at the solstice) as is done in the film is circular reasoning: The film claims that Jesus is astrological because his birthday falls on an astrological day, however in reality the day was chosen to BECAUSE of the coincident, pre-existing astrological similarities. Jesus doesn't represent astrology: the astrology was co-opted to represent Jesus.
There are several other arguments in the film that also rely on convenient coincidences or circular reasoning. One that springs to mind is the argument that Moses's anger toward Jews worshipping a bull idol (when he returned from the mountain) was because, astrologically, a new age was beginning and the new age (Aries, the ram) was replacing the old (Taurus, the bull). The film claims that this is why Jews blow into a ram's horn. A simpler explanation is that the Hebrew people farmed sheep, and thus would be quite familiar with rams horns and use what's at hand.
Overall the film is entertaining and highlights some amusing similarities between Christianity and Astrology. But since the only evidence in the film is circular, this film falls short of being a documentary or research paper, and instead is merely sensationalist and reminiscent of a conspiracy theory.